Transformed!
Compose Yourself
So Basic
Decompose Yourself
Let's Be Rational
100
Write the equation for the function that shifts
y=x^2
4 units to the right and 3 units down.
What is
f(x)=(x-4)^2-3 ?
100
f(x) = 3x
g(x) = -4x
find f(g(x))
-12x
100
f(x)=3x-4 and g(x)=2x-1
This is (f+g)(3)
What is 10?
100
f(x)= 20x2+ 11
Write equations for g(x) and h(x) so that f is the composition g(h(x))
One possible example:
g(x)=x+11
h(x)=20x2
100
f(x)=3/(x+2)
g(x)=x-2
Find and Simplify
(f/g)(x)
What is
3/((x-2)(x+2))?
200
How is the graph of
y=sqrt(x)
transformed to create the graph of
y=-3sqrt(x)-4
It is reflected in the x axis, vertically stretched by a factor of 3, and shifted down four units.
200
f(x)= x2+9x
g(x)=(x+6)
find (f o g)(-2)
What is 52?
200
f(x) = 2x2-4 and h(x)=3x+1
This is (f-h)(x) in standard form.
What is 2x^2-3x-5 ?
200
g(x)=3(x-2)3-8
Write equations for f(x) and h(x) so that g is the composition h(f(x))
One possible answer is
f(x)=x-2
h(x)=3x3-8
200
Add the following expressions
3/(x+4)+(2x)/(x-2)
What is (2x^2+11x-6)/((x+4)(x-2))
300
The graph of f(x) is the solid black graph. What transformation does the dotted graph represent?
What is
f(-x)-5 ?
300
f(x)= –2x + 9
g(x) =
sqrt(x+4)
find (g o f)(x)
sqrt(-2x+13)
300
g(x)=3x^2-27
and f(x)=4x+1. This is the domain of (g/f)(x).
What is (-oo,-1/4)U(-1/4,oo) ?
300
h(x)=3sin(2x)
Write functions f(x) and g(x) so that h(x) is the composition f(g(x))
One possibility is
f(x)=3sin(x)
g(x)=2x
300
Find f(x)-g(x) when f(x)=7x+3 and g(x)=
(x-3)/7
What is (48x+24)/7 ?
400
Use a parent function and transformations to write an equation for the graph shown here.
What is f(x)=-1/2(x-4)^2+1
400
f(x) = 3x² + 6
g(x)=sqrt(x)
This is f(g(10)).
What is 36?
400
g(x)=3x^2-48
f(x)=2x+5
This is the domain of
(f/g)(x)
What is
{RR, xne-4, xne4}?
400
h(x)=3e^sinx
Write functions f(x) and g(x) so that h(x) is the composition g(f(x)).
f(x)=sinx
g(x)=3ex
400
Multiply:
(x^2-4)*(5x-1)/(x+2)
What is (5x-1)(x-2) ?
Also correct:
5x^2-11x+2
500
Use a parent function and function transformations to write an equation for the function shown here.
What is f(x)=-1/(x+2)^2 ?
500
What is f(g(h(x)))?
f(x)=3x+2
g(x)=sqrt(x)
h(x)=5-x
What is
3sqrt(5-x)+2 ?
500
Use the graphs to find g(3)-2f(1).
What is -2?
500
f(x)=x-6. Write a function g(x) so that f(x) is the composition g(g(x))
g(x)=x-3
500
Divide!
(x^2+3x-4)/(3x-3)
What is (x+4)/3 ?